Question

A person rows a boat 10 kms along the stream in 30 minutes and returns to the starting point in 40 minutes. The speed of the stream is:

• A. 17.5 km/h
• B. 2.5 km/h
• C. 5 km/h
• D. 15 km/h

Hint:

Remember these two key formulas: Speed of stream = (Downstream Speed - Upstream Speed) / 2 Speed of boat in still water = (Downstream Speed + Upstream Speed) / 2 These can save a lot of time in boat and stream problems.

Answer 1

The Correct Option is B

Step 1: Conceptual Foundation:
This problem pertains to the concept of relative speed as applied to boat and stream scenarios.
Downstream velocity (\(S_D\)) is defined as the speed of the boat in still water (\(S_B\)) augmented by the speed of the stream (\(S_S\)).
Upstream velocity (\(S_U\)) is the speed of the boat in still water (\(S_B\)) minus the speed of the stream (\(S_S\)).
The speed of the stream (\(S_S\)) can be derived using the formula \(S_S = \frac{S_D - S_U}{2}\).
Step 2: Methodological Framework:
1. Determine the downstream velocity (\(S_D\)).2. Determine the upstream velocity (\(S_U\)).3. Employ the derived formula to ascertain the stream's speed.Ensure that temporal units are converted from minutes to hours.
Step 3: Algorithmic Execution:
Downstream Traversal (with the current):
Distance covered: 10 km.
Time elapsed: 30 minutes, which converts to \( \frac{30}{60} \) hours or 0.5 hours.
Downstream velocity (\(S_D\)) = \( \frac{\text{Distance}}{\text{Time}} = \frac{10}{0.5} = 20 \) km/h.
Upstream Traversal (against the current):
Distance covered: 10 km.
Time elapsed: 40 minutes, which converts to \( \frac{40}{60} \) hours or \( \frac{2}{3} \) hours.
Upstream velocity (\(S_U\)) = \( \frac{\text{Distance}}{\text{Time}} = \frac{10}{2/3} = 10 \times \frac{3}{2} = 15 \) km/h.
Stream Velocity Calculation:
Speed of stream (\(S_S\)) = \( \frac{S_D - S_U}{2} \)
Substituting the calculated values: \(S_S = \frac{20 - 15}{2} = \frac{5}{2} = 2.5 \) km/h.
Step 4: Conclusion:
The calculated speed of the stream is 2.5 km/h.